Electron. J. Differential Equations, Vol. 2018 (2018), No. 03, pp. 1-21.

Asymptotic behavior of pullback attractors for non-autonomous micropolar fluid flows in 2D unbounded domains

Wenlong Sun, Yeping Li

Abstract:
In this article, we investigate the pullback asymptotic behavior of solutions for a non-autonomous micropolar fluid flows in 2D unbounded channel-like domains. First, applying the technique of truncation functions, decomposition of spatial domain, and the energy method, we show the existence of the pullback attractor in the space $\widehat{H}(\Omega)$ (has L^2-regularity). In fact, we can deduce the existence of pullback attractor in space $\widehat{V}(\Omega)$ (has H^1-regularity). Also the tempered behavior of the pullback attractor is verified. Moreover, when the spatial domain varies from $\Omega_m$ ( $\{\Omega_m\}_{m=1}^{\infty}$ be an expanding sequence of simply connected, bounded and smooth subdomains of $\Omega$ such that $\cup_{m=1}^{\infty}\Omega_m = \Omega$) to $\Omega$, the upper semicontinuity of the pullback attractor is discussed.

Submitted March 6, 2017. Published January 4, 2018.
Math Subject Classifications: 35B40, 35B41, 35Q30.
Key Words: Micropolar fluid flow; pullback attractor; truncation function; tempered behavior; upper semicontinuity.

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  Wenlong Sun
Department of Mathematics
East China University of Science and Technology
Shanghai 200237, China
email: wenlongsun1988@163.com
Yeping Li
Department of Mathematics
East China University of Science and Technology
Shanghai 200237, China
email: yplee@ecust.edu.cn

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